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With recent constraints on the propagation speed of gravitational waves, the class of scalar-tensor theories has significantly been reduced. We consider one of the surviving models still relevant for cosmology and investigate its radiative stability. The model contains operators with explicit breaking of the Galileon symmetry and we study whether they harm the re-organization of the effective field theory. Within the regime of validity we establish a non-renormalization theorem and show explicitly that the quantum corrections, to one-loop, do not detune the classical Lagrangian generating suppressed counterterms. This is striking since the non-renormalization theorem is established in the presence of a genuine Galileon symmetry breaking term.
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Determining the most general, consistent scalar tensor theory of gravity is important for building models of inflation and dark energy. In this work we investigate the number of degrees of freedom present in the theory of beyond Horndeski. We discuss how to construct the theory from the extrinsic curvature of the constant scalar field hypersurface, and find a simple expression for the action which guarantees the existence of the primary constraint necessary to avoid the Ostrogradsky instability. Our analysis is completely gauge-invariant. However we confirm that, mixing together beyond Horndeski with a different order of Horndeski, obstructs the construction of this primary constraint. Instead, when the mixing is between actions of the same order, the theory can be mapped to Horndeski through a generalised disformal transformation. This mapping however is impossible with beyond Horndeski alone, since we find that the theory is invariant under such a transformation. The picture that emerges is that beyond Horndeski is a healthy but isolated theory: combined with Horndeski, it either becomes Horndeski, or likely propagates a ghost.
We review the effective field theory of modified gravity in which the Lagrangian involves three dimensional geometric quantities appearing in the 3+1 decomposition of space-time. On the flat isotropic cosmological background we expand a general action up to second order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories-- including Horndeski theory/its recent generalizations and the projectable/non-projectab
We study the instability of de Sitter space-time (dS) under thermal radiation in different vacua. For this purpose we model the interaction between thermal radiation and unknown ultraviolet physics as a scattering process inside the horizon. Then we argue that the mode function solution of a scalar field in four-dimensional dS can be separated into the incoming and outgoing modes. Different vacua for dS are realized by different combinations of positive frequency modes assigned to each solution. For a minimally coupled massless scalar field, we explicitly compute the behavior of the mode function and the corresponding energy-momentum tensor in the Unruh vacuum near the horizon, and find that the horizon area increases (decreases) in time when the incoming (outgoing) mode contributes to thermal flux.
The most robust prediction of inflationary cosmology is the existence of a red tilt for the spectrum of curvature fluctuations that is experimentally of order $0.04$. The tilt is derived solving the exact equation for quantum fluctuations in a quasi de Sitter background defined by a equation of state $epsilon equiv frac{(p+rho)}{rho}$ with $epsilon$ small but non vanishing. The experimental data selects among the different quasi de Sitter inflaton potentials. The origin of the lack of scale invariance associated with the tilt is however classical in essence and parametrized by the slow roll of the inflaton potential. Here we present a purely quantum mechanical and model independent derivation of the tilt. This derivation is based on two basic observations: first, the correlator for gauge invariant variables is related to the {it quantum Fisher function} measuring the quantum dependence of the family of pure de Sitter vacua on the energy scale parameter; second, this quantum Fisher function has a non vanishing scale dependent red tilt that, at the energy scales of physical interest, fits the effective quasi de Sitter prediction as well as the experimental value. This is a result that is model independent and only based on the quantum features of the family of de Sitter vacua.
We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation approach of the covariant effective action at 1-loop. We show that the consideration of gravitational effects in combination with the non-linear derivative structure of the theory reveals new interactions at the perturbative level, which manifest themselves as higher-operators in the associated effective action, which relevance is controlled by appropriate ratios of the cosmological vacuum and the Galileon mass scale. The significance and concept of the covariant approach in this context is discussed, while all calculations are explicitly presented.
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